A website affiliated with Chechen rebels has released a video in which insurgent leader Doku Umarov claims responsibility for last month's deadly suicide bombing at Russia's largest airport and threatens more bloodshed if Russia does not leave the region.

Flags flew at half-mast on government buildings and at the Kremlin as a day of national mourning for the victims of the Moscow tube blasts began.

Russian Prime Minister Vladimir Putin is vowing to "destroy those responsible" for the Moscow metro suicide attacks.

The Department of Foreign Affairs is contacting Irish citizens in Moscow, warning them of the danger of further attacks, in the wake of two suicide bombings in the Russian capital.

A statement on a website sympathetic to Chechen rebels says the militants have claimed responsibility for last week’s Russian train bombing that killed at least 26 people and injured scores of others.

The younger brother of Chechen rebel leader Doku Umarov has turned himself in, a government spokesman said today, denying an earlier claim that Umarov himself had surrendered.

Russian and Chechen regional forces battled fighters holed up in an apartment building in the Chechen capital of Grozny today, killing at least five fighters and leaving at least two federal troops dead, officials said.